Details

analyze1.8s (2.9%)

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)

sample1.6s (2.5%)

Algorithm

1×

intervals

Results

1.5s	133×	body	8192	exit
75.0ms	256×	body	128	valid
10.0ms	389×	pre	128	true

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify55.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

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)

localize60.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)

rewrite1.3s (2%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

36×	`*-un-lft-identity_binary64_3147`
28×	`add-sqr-sqrt_binary64_3169`
24×	`add-log-exp_binary64_3186` `cancel-sign-sub-inv_binary64_3113`
16×	`associate--l+_binary64_3084`
12×	`diff-log_binary64_3239` `add-cube-cbrt_binary64_3182` `distribute-lft-out--_binary64_3099`
8×	`sub-neg_binary64_3140` `difference-of-squares_binary64_3116`
4×	`pow1_binary64_3208` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `flip3--_binary64_3151` `flip--_binary64_3122` `difference-of-sqr-1_binary64_3117` `associate--l-_binary64_3085`

Counts

4 → 100

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series223.0ms (0.3%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (-.f64 1 z) 1)
41.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)
39.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.3s (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Error

1.8b

Counts

114 → 2

Compiler

Compiled 14117 to 11932 computations (15.5% saved)

localize69.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)

rewrite1.3s (2.1%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

36×	`*-un-lft-identity_binary64_3147`
28×	`add-sqr-sqrt_binary64_3169`
24×	`add-log-exp_binary64_3186` `cancel-sign-sub-inv_binary64_3113`
16×	`associate--l+_binary64_3084`
12×	`diff-log_binary64_3239` `add-cube-cbrt_binary64_3182` `distribute-lft-out--_binary64_3099`
8×	`sub-neg_binary64_3140` `difference-of-squares_binary64_3116`
4×	`pow1_binary64_3208` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `flip3--_binary64_3151` `flip--_binary64_3122` `difference-of-sqr-1_binary64_3117` `associate--l-_binary64_3085`

Counts

4 → 100

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 13296 to 10600 computations (20.3% saved)

series234.0ms (0.4%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

43.0ms	(-.f64 (-.f64 1 z) 1)
43.0ms	(-.f64 (-.f64 1 z) 1)
43.0ms	(-.f64 (-.f64 1 z) 1)
41.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4500 to 3814 computations (15.2% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.3s (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Error

1.8b

Counts

114 → 2

Compiler

Compiled 14438 to 11373 computations (21.2% saved)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

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	(+.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	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite476.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

19×	`*-un-lft-identity_binary64_3147`
18×	`add-log-exp_binary64_3186`
10×	`add-exp-log_binary64_3185`
9×	`sum-log_binary64_3238` `pow1_binary64_3208` `add-cbrt-cube_binary64_3183` `distribute-lft-out_binary64_3098`
8×	`frac-add_binary64_3155`
7×	`prod-exp_binary64_3196`
5×	`add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169` `flip3-+_binary64_3150` `flip-+_binary64_3121`
4×	`associate-r_binary64_3087`
3×	`cbrt-unprod_binary64_3180`
2×	`associate-+l+_binary64_3080` `+-commutative_binary64_3077` `pow-prod-down_binary64_3218` `sqrt-pow1_binary64_3165`
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` `associate-l_binary64_3088` `exp-sum_binary64_3193` `*-commutative_binary64_3078`

Counts

4 → 70

Calls

4 calls:

41.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
23.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6200 to 4800 computations (22.6% saved)

series365.0ms (0.6%)

Error

1.1b

Counts

4 → 20

Calls

4 calls:

192.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
54.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
37.0ms	(+.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 3676 to 2954 computations (19.6% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5563	2799

prune524.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	86	6	92

Error

1.1b

Counts

92 → 6

Compiler

Compiled 7897 to 6090 computations (22.9% saved)

localize56.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.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	(.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	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite942.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

49×	`*-un-lft-identity_binary64_3147`
48×	`add-log-exp_binary64_3186`
34×	`sum-log_binary64_3238` `distribute-lft-out_binary64_3098`
32×	`frac-add_binary64_3155`
10×	`add-exp-log_binary64_3185`
9×	`pow1_binary64_3208` `add-cbrt-cube_binary64_3183`
8×	`flip3-+_binary64_3150` `flip-+_binary64_3121`
7×	`prod-exp_binary64_3196`
5×	`add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169`
4×	`associate-r_binary64_3087`
3×	`cbrt-unprod_binary64_3180`
2×	`pow-prod-down_binary64_3218` `sqrt-pow1_binary64_3165` `associate-+l+_binary64_3080` `+-commutative_binary64_3077`
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` `associate-l_binary64_3088` `exp-sum_binary64_3193` `*-commutative_binary64_3078`

Counts

4 → 86

Calls

4 calls:

118.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.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)))
55.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
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)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 9783 to 7705 computations (21.2% saved)

series429.0ms (0.7%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

202.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
92.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.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)))
57.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3624 to 2888 computations (20.3% saved)

simplify121.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4957	7930
1	4957	7930

prune809.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Error

0.2b

Counts

116 → 7

Compiler

Compiled 10843 to 8438 computations (22.2% saved)

regimes754.0ms (1.2%)

Accuracy

Total 0.2b remaining (42.8%)

Threshold costs 0.2b (42.8%)

Compiler

Compiled 11266 to 9456 computations (16.1% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	155	460
1	155	460

end0.0ms (0%)

sample49.8s (77.9%)

Algorithm

1×

intervals

Results

42.2s	3835×	body	8192	exit
2.4s	8000×	body	128	valid
438.0ms	11895×	pre	128	true
22.0ms	60×	body	128	invalid

Compiler

Compiled 5939 to 4982 computations (16.1% saved)

Details

analyze1.8s (2.9%)

sample1.6s (2.5%)

simplify55.0ms (0.1%)

prune12.0ms (0%)

localize60.0ms (0.1%)

rewrite1.3s (2%)

series223.0ms (0.3%)

simplify82.0ms (0.1%)

prune1.3s (2.1%)

localize69.0ms (0.1%)

rewrite1.3s (2.1%)

series234.0ms (0.4%)

simplify86.0ms (0.1%)

prune1.3s (2%)

localize58.0ms (0.1%)

rewrite476.0ms (0.7%)

series365.0ms (0.6%)

simplify68.0ms (0.1%)

prune524.0ms (0.8%)

localize56.0ms (0.1%)

rewrite942.0ms (1.5%)

series429.0ms (0.7%)

simplify121.0ms (0.2%)

prune809.0ms (1.3%)

regimes754.0ms (1.2%)

bsearch0.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample49.8s (77.9%)

Profiling