Details

analyze1.8s (3.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.3s (2.2%)

Algorithm

1×

intervals

Results

1.2s	108×	body	8192	exit
72.0ms	256×	body	128	valid
5.0ms	365×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify51.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune12.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite829.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

53×	`add-log-exp_binary64_3186` `*-un-lft-identity_binary64_3147`
50×	`frac-add_binary64_3155`
37×	`sum-log_binary64_3238` `distribute-lft-out_binary64_3098`
12×	`flip3-+_binary64_3150` `flip-+_binary64_3121`
7×	`pow1_binary64_3208`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169`
3×	`associate-+l+_binary64_3080` `+-commutative_binary64_3077`
2×	`sqrt-pow1_binary64_3165`
1×	`pow1/2_binary64_3227` `pow-prod-down_binary64_3218` `sqrt-prod_binary64_3163`

Counts

4 → 86

Calls

4 calls:

95.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
39.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 10358 to 8199 computations (20.8% saved)

series247.0ms (0.4%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

97.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
51.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
36.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2948 to 2303 computations (21.9% saved)

simplify111.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5057	8268

prune893.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Error

0.2b

Counts

112 → 4

Compiler

Compiled 11551 to 9016 computations (21.9% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 z)
0.4b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite209.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64_3169`
15×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
14×	`add-exp-log_binary64_3185`
13×	`add-cbrt-cube_binary64_3183`
11×	`pow1_binary64_3208`
9×	`times-frac_binary64_3153`
8×	`prod-exp_binary64_3196`
7×	`associate-r_binary64_3087`
4×	`add-log-exp_binary64_3186` `cbrt-unprod_binary64_3180` `associate-l_binary64_3088`
3×	`pow-prod-down_binary64_3218` `associate-/l_binary64_3092` `associate-/r_binary64_3091`
2×	`sqrt-pow1_binary64_3165` `*-commutative_binary64_3078`
1×	`pow1/2_binary64_3227` `sqrt-prod_binary64_3163` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `pow-sub_binary64_3223` `associate-r/_binary64_3089` `associate-l/_binary64_3090` `exp-sum_binary64_3193` `div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144` `unswap-sqr_binary64_3115`

Counts

4 → 77

Calls

4 calls:

17.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms	(*.f64 PI.f64 z)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3328 to 2232 computations (32.9% saved)

series208.0ms (0.4%)

Error

0.1b

Counts

4 → 10

Calls

4 calls:

131.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
32.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
23.0ms	(*.f64 PI.f64 z)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1186 to 933 computations (21.3% saved)

simplify102.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4932	1475
1	4932	1475

prune211.0ms (0.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	79	12	91

Error

0.0b

Counts

91 → 12

Compiler

Compiled 4270 to 2948 computations (31% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.3b	(.f64 (/.f64 1 z) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite481.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

94×	`add-exp-log_binary64_3185`
80×	`prod-exp_binary64_3196`
43×	`add-cbrt-cube_binary64_3183`
28×	`associate-*r/_binary64_3089`
24×	`cbrt-unprod_binary64_3180`
20×	`pow1_binary64_3208`
17×	`associate-l_binary64_3088` `frac-times_binary64_3157`
16×	`add-sqr-sqrt_binary64_3169`
14×	`add-cube-cbrt_binary64_3182` `-un-lft-identity_binary64_3147` `associate-l/_binary64_3090`
12×	`div-exp_binary64_3198`
11×	`pow-sub_binary64_3223`
9×	`pow-prod-down_binary64_3218` `times-frac_binary64_3153`
8×	`associate-r_binary64_3087` `flip3-+_binary64_3150` `frac-add_binary64_3155` `flip-+_binary64_3121`
6×	`1-exp_binary64_3191` `rec-exp_binary64_3197`
5×	`pow-to-exp_binary64_3216` `pow-exp_binary64_3215`
4×	`add-log-exp_binary64_3186` `cbrt-undiv_binary64_3181` `distribute-rgt-in_binary64_3097` `distribute-lft-in_binary64_3096`
3×	`*-commutative_binary64_3078`
2×	`sqrt-pow1_binary64_3165`
1×	`pow1/2_binary64_3227` `sqrt-prod_binary64_3163` `exp-sum_binary64_3193` `div-inv_binary64_3144` `unswap-sqr_binary64_3115`

Counts

4 → 130

Calls

4 calls:

40.0ms	(.f64 (/.f64 1 z) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6210 to 4919 computations (20.8% saved)

series341.0ms (0.6%)

Error

Counts

4 → 13

Calls

4 calls:

178.0ms	(.f64 (/.f64 1 z) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (.f64 z 58027045549583850709031327/132816557330708771635200)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
120.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
21.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1433 to 1199 computations (16.3% saved)

simplify141.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5013	5701

prune373.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	147	8	155

Error

Counts

155 → 8

Compiler

Compiled 6192 to 4897 computations (20.9% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64)))) (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (*.f64 z 58027045549583850709031327/132816557330708771635200)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))) z)
0.2b	(*.f64 z 58027045549583850709031327/132816557330708771635200)
1.0b	(.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite291.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-exp-log_binary64_3185`
25×	`add-cbrt-cube_binary64_3183`
20×	`prod-exp_binary64_3196`
11×	`pow1_binary64_3208` `add-sqr-sqrt_binary64_3169`
10×	`cbrt-unprod_binary64_3180` `associate-*r/_binary64_3089`
9×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147` `associate-/l/_binary64_3094`
7×	`associate-l/_binary64_3090` `associate-l*_binary64_3088`
6×	`pow-sub_binary64_3223` `div-exp_binary64_3198`
4×	`add-log-exp_binary64_3186` `associate-r_binary64_3087` `cbrt-undiv_binary64_3181` `flip3-+_binary64_3150` `frac-add_binary64_3155` `frac-times_binary64_3157` `flip-+_binary64_3121`
3×	`pow-prod-down_binary64_3218` `times-frac_binary64_3153` `associate-/r*_binary64_3091`
2×	`sqrt-pow1_binary64_3165` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `*-commutative_binary64_3078`
1×	`pow1/2_binary64_3227` `sqrt-prod_binary64_3163` `exp-sum_binary64_3193` `unswap-sqr_binary64_3115` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144` `associate-/l*_binary64_3092`

Counts

4 → 86

Calls

4 calls:

32.0ms	(/.f64 (.f64 (.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64)))) (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (*.f64 z 58027045549583850709031327/132816557330708771635200)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))) z)
16.0ms	(.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))))
4.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
2.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 3777 to 2946 computations (22% saved)

series346.0ms (0.6%)

Error

Counts

4 → 13

Calls

4 calls:

176.0ms	(/.f64 (.f64 (.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64)))) (+.f64 (+.f64 777369958913643152449373/2951479051793528258560 (*.f64 z 58027045549583850709031327/132816557330708771635200)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))) z)
126.0ms	(.f64 (exp.f64 (+.f64 -15/2 z)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 PI.f64))))
19.0ms	(*.f64 z 58027045549583850709031327/132816557330708771635200)
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 1393 to 1159 computations (16.8% saved)

simplify99.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4991	2763
1	4991	2763

prune213.0ms (0.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	101	6	107

Error

Counts

107 → 6

Compiler

Compiled 3679 to 2882 computations (21.7% saved)

regimes693.0ms (1.2%)

Accuracy

Total 0.5b remaining (94.5%)

Threshold costs 0.5b (94.5%)

Compiler

Compiled 9934 to 8052 computations (18.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	113	133
1	113	133

end0.0ms (0%)

sample49.9s (84.6%)

Algorithm

1×

intervals

Results

43.0s	3913×	body	8192	exit
2.4s	8000×	body	128	valid
210.0ms	11997×	pre	128	true
27.0ms	84×	body	128	invalid

Compiler

Compiled 5052 to 4098 computations (18.9% saved)

Details

analyze1.8s (3.1%)

sample1.3s (2.2%)

simplify51.0ms (0.1%)

prune12.0ms (0%)

localize54.0ms (0.1%)

rewrite829.0ms (1.4%)

series247.0ms (0.4%)

simplify111.0ms (0.2%)

prune893.0ms (1.5%)

localize28.0ms (0%)

rewrite209.0ms (0.4%)

series208.0ms (0.4%)

simplify102.0ms (0.2%)

prune211.0ms (0.4%)

localize23.0ms (0%)

rewrite481.0ms (0.8%)

series341.0ms (0.6%)

simplify141.0ms (0.2%)

prune373.0ms (0.6%)

localize22.0ms (0%)

rewrite291.0ms (0.5%)

series346.0ms (0.6%)

simplify99.0ms (0.2%)

prune213.0ms (0.4%)

regimes693.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample49.9s (84.6%)

Profiling