Details

analyze2.3s (2.7%)

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)

sample1.9s (2.3%)

Algorithm

1×

intervals

Results

1.8s	134×	body	8192	exit
88.0ms	256×	body	128	valid
8.0ms	392×	pre	128	true
1.0ms	2×	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 (44.0ms)

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

1.7b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize72.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(-.f64 (-.f64 1 z) 1)
5.2b	(-.f64 (-.f64 1 z) 1)
5.2b	(-.f64 (-.f64 1 z) 1)
5.2b	(-.f64 (-.f64 1 z) 1)

rewrite1.2s (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

36×	`*-un-lft-identity_binary64_2465`
28×	`add-sqr-sqrt_binary64_2487`
24×	`add-log-exp_binary64_2504` `cancel-sign-sub-inv_binary64_2431`
16×	`associate--l+_binary64_2402`
12×	`diff-log_binary64_2557` `add-cube-cbrt_binary64_2500` `distribute-lft-out--_binary64_2417`
8×	`sub-neg_binary64_2458` `difference-of-squares_binary64_2434`
4×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3--_binary64_2469` `flip--_binary64_2440` `difference-of-sqr-1_binary64_2435` `associate--l-_binary64_2403`

Counts

4 → 100

Calls

4 calls:

16.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.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)

series288.0ms (0.3%)

Error

1.7b

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.f64 (-.f64 1 z) 1)
47.0ms	(-.f64 (-.f64 1 z) 1)
46.0ms	(-.f64 (-.f64 1 z) 1)
46.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.5s (1.8%)

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

1.7b

Counts

114 → 2

Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize70.0ms (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)))

rewrite1.0s (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

53×	`add-log-exp_binary64_2504` `*-un-lft-identity_binary64_2465`
50×	`frac-add_binary64_2473`
37×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
12×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
7×	`pow1_binary64_2526`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
3×	`associate-+l+_binary64_2398` `+-commutative_binary64_2395`
2×	`sqrt-pow1_binary64_2483`
1×	`pow1/2_binary64_2545` `pow-prod-down_binary64_2536` `sqrt-prod_binary64_2481`

Counts

4 → 86

Calls

4 calls:

110.0ms	(+.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)))
48.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
30.0ms	(+.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)

series296.0ms (0.3%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

101.0ms	(+.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)))
73.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
40.0ms	(+.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)

simplify143.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5057	8268

prune999.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	104	8	112

Error

0.2b

Counts

112 → 8

Compiler

Compiled 12556 to 9845 computations (21.6% saved)

localize136.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite4.1s (4.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

24×	`add-log-exp_binary64_2504` `*-un-lft-identity_binary64_2465`
12×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
8×	`flip3-+_binary64_2468` `frac-add_binary64_2473` `flip-+_binary64_2439`
4×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `associate-+r+_binary64_2397` `+-commutative_binary64_2395`

Counts

4 → 68

Calls

4 calls:

45.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
31.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 27532 to 22789 computations (17.2% saved)

series1.4s (1.6%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

176.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
154.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
149.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
143.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

Compiler

Compiled 21456 to 17869 computations (16.7% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4967	2192
1	4967	2192

prune5.3s (6.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Error

0.2b

Counts

100 → 8

Compiler

Compiled 37447 to 30939 computations (17.4% saved)

localize69.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.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)))
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	(+.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	(sqrt.f64 (*.f64 PI.f64 2))

rewrite1.2s (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

62×	`add-log-exp_binary64_2504` `*-un-lft-identity_binary64_2465`
44×	`sum-log_binary64_2556` `distribute-lft-out_binary64_2416`
38×	`frac-add_binary64_2473`
11×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
7×	`pow1_binary64_2526`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
3×	`associate-+l+_binary64_2398` `+-commutative_binary64_2395`
2×	`sqrt-pow1_binary64_2483`
1×	`pow1/2_binary64_2545` `pow-prod-down_binary64_2536` `sqrt-prod_binary64_2481`

Counts

4 → 88

Calls

4 calls:

127.0ms	(+.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)))
76.0ms	(+.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)))
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)))
5.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 10423 to 8248 computations (20.9% saved)

series342.0ms (0.4%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

101.0ms	(+.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)))
94.0ms	(+.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)))
48.0ms	(+.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 3436 to 2677 computations (22.1% saved)

simplify128.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4898	7768
1	4898	7768

prune898.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Error

0.2b

Counts

126 → 7

Compiler

Compiled 10997 to 8501 computations (22.7% saved)

regimes830.0ms (1%)

Accuracy

Total 0.2b remaining (39.3%)

Threshold costs 0.2b (39.3%)

Compiler

Compiled 10504 to 8748 computations (16.7% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	117
1	105	117

end0.0ms (0%)

sample1.0min (71.4%)

Algorithm

1×

intervals

Results

52.7s	3860×	body	8192	exit
3.0s	8000×	body	128	valid
260.0ms	11946×	pre	128	true
34.0ms	86×	body	128	invalid

Compiler

Compiled 5329 to 4438 computations (16.7% saved)

Details

analyze2.3s (2.7%)

sample1.9s (2.3%)

simplify51.0ms (0.1%)

prune12.0ms (0%)

localize72.0ms (0.1%)

rewrite1.2s (1.4%)

series288.0ms (0.3%)

simplify94.0ms (0.1%)

prune1.5s (1.8%)

localize70.0ms (0.1%)

rewrite1.0s (1.2%)

series296.0ms (0.3%)

simplify143.0ms (0.2%)

prune999.0ms (1.2%)

localize136.0ms (0.2%)

rewrite4.1s (4.8%)

series1.4s (1.6%)

simplify80.0ms (0.1%)

prune5.3s (6.2%)

localize69.0ms (0.1%)

rewrite1.2s (1.4%)

series342.0ms (0.4%)

simplify128.0ms (0.1%)

prune898.0ms (1.1%)

regimes830.0ms (1%)

bsearch0.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample1.0min (71.4%)

Profiling