Details

analyze1.7s (1.8%)

Algorithm

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)

sample2.9s (3%)

Algorithm

1×

intervals

Results

2.8s	129×	body	8192	exit
87.0ms	256×	body	128	valid
8.0ms	388×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify211.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4776	115
1	4776	115

prune23.0ms (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

Merged error: 1.8b

Counts

2 → 2

Compiler

Compiled 468 to 403 computations (13.9% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(-.f64 (-.f64 1 z) 1)
5.4b	(-.f64 (-.f64 1 z) 1)
5.4b	(-.f64 (-.f64 1 z) 1)
5.4b	(-.f64 (-.f64 1 z) 1)

rewrite67.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_2831`
28×	`add-sqr-sqrt_binary64_2853`
24×	`add-log-exp_binary64_2870` `cancel-sign-sub-inv_binary64_2797`
16×	`associate--l+_binary64_2768`
12×	`add-cube-cbrt_binary64_2866` `distribute-lft-out--_binary64_2783` `diff-log_binary64_2923`
8×	`sub-neg_binary64_2824` `difference-of-squares_binary64_2800`
4×	`pow1_binary64_2892` `add-cbrt-cube_binary64_2867` `flip3--_binary64_2835` `difference-of-sqr-1_binary64_2801` `flip--_binary64_2806` `add-exp-log_binary64_2869` `associate--l-_binary64_2769`

Counts

4 → 100

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)

series73.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4806	704
1	4806	704

prune1.1s (1.1%)

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

Merged error: 1.8b

Counts

114 → 2

Compiler

Compiled 15068 to 12769 computations (15.3% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(-.f64 (-.f64 1 z) 1)
5.4b	(-.f64 (-.f64 1 z) 1)
5.4b	(-.f64 (-.f64 1 z) 1)
42.6b	(cbrt.f64 (pow.f64 (neg.f64 z) 3))

rewrite71.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_2831`
29×	`add-sqr-sqrt_binary64_2853`
26×	`cbrt-prod_binary64_2862`
19×	`add-log-exp_binary64_2870`
18×	`cancel-sign-sub-inv_binary64_2797`
17×	`add-cube-cbrt_binary64_2866`
12×	`associate--l+_binary64_2768`
10×	`unpow-prod-down_binary64_2910` `cube-prod_binary64_2859`
9×	`distribute-lft-out--_binary64_2783` `diff-log_binary64_2923`
6×	`sub-neg_binary64_2824` `distribute-rgt-neg-in_binary64_2789` `difference-of-squares_binary64_2800` `distribute-lft-neg-in_binary64_2788`
4×	`pow1_binary64_2892` `add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869`
3×	`flip3--_binary64_2835` `difference-of-sqr-1_binary64_2801` `flip--_binary64_2806` `associate--l-_binary64_2769`
2×	`neg-mul-1_binary64_2827`
1×	`pow1/3_binary64_2913` `sqr-pow_binary64_2803` `cube-mult_binary64_2861` `rem-cbrt-cube_binary64_2855` `unpow3_binary64_2897`

Counts

4 → 110

Calls

4 calls:

16.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
5.0ms	(cbrt.f64 (pow.f64 (neg.f64 z) 3))

series88.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt.f64 (pow.f64 (neg.f64 z) 3))
18.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4854	807
1	4854	807

prune1.3s (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	122	2	124

Merged error: 1.8b

Counts

124 → 2

Compiler

Compiled 15863 to 13269 computations (16.4% saved)

localize55.0ms (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 (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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite103.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_2831`
18×	`add-log-exp_binary64_2870`
10×	`add-exp-log_binary64_2869`
9×	`pow1_binary64_2892` `add-cbrt-cube_binary64_2867` `distribute-lft-out_binary64_2782` `sum-log_binary64_2922`
8×	`frac-add_binary64_2839`
7×	`prod-exp_binary64_2880`
5×	`add-cube-cbrt_binary64_2866` `flip3-+_binary64_2834` `add-sqr-sqrt_binary64_2853` `flip-+_binary64_2805`
4×	`associate-r_binary64_2771`
3×	`cbrt-unprod_binary64_2864`
2×	`pow-prod-down_binary64_2902` `+-commutative_binary64_2761` `sqrt-pow1_binary64_2849` `associate-+l+_binary64_2764`
1×	`pow-exp_binary64_2899` `pow1/2_binary64_2911` `-commutative_binary64_2762` `exp-sum_binary64_2877` `associate-l/_binary64_2774` `pow-sub_binary64_2907` `pow-to-exp_binary64_2900` `associate-l_binary64_2772` `sqrt-prod_binary64_2847` `associate-*r/_binary64_2773`

Counts

4 → 70

Calls

4 calls:

38.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
26.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
18.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series278.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

208.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
40.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
29.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify60.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5515	2608

prune656.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	76	6	82

Merged error: 1.1b

Counts

82 → 6

Compiler

Compiled 12566 to 10057 computations (20% saved)

localize57.0ms (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 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 (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))

rewrite220.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_2831`
48×	`add-log-exp_binary64_2870`
34×	`distribute-lft-out_binary64_2782` `sum-log_binary64_2922`
32×	`frac-add_binary64_2839`
10×	`add-exp-log_binary64_2869`
9×	`pow1_binary64_2892` `add-cbrt-cube_binary64_2867`
8×	`flip3-+_binary64_2834` `flip-+_binary64_2805`
7×	`prod-exp_binary64_2880`
5×	`add-cube-cbrt_binary64_2866` `add-sqr-sqrt_binary64_2853`
4×	`associate-r_binary64_2771`
3×	`cbrt-unprod_binary64_2864`
2×	`pow-prod-down_binary64_2902` `+-commutative_binary64_2761` `sqrt-pow1_binary64_2849` `associate-+l+_binary64_2764`
1×	`pow-exp_binary64_2899` `pow1/2_binary64_2911` `-commutative_binary64_2762` `exp-sum_binary64_2877` `associate-l/_binary64_2774` `pow-sub_binary64_2907` `pow-to-exp_binary64_2900` `associate-l_binary64_2772` `sqrt-prod_binary64_2847` `associate-*r/_binary64_2773`

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)))
19.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series318.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

186.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
93.0ms	(+.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)))
39.0ms	(+.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))

simplify122.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4936	7503
1	4936	7503

prune899.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.2b

Counts

102 → 6

Compiler

Compiled 14036 to 11155 computations (20.5% saved)

regimes59.0ms (0.1%)

Compiler: Compiled 534 to 444 computations (16.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	117
1	105	117

end0.0ms (0%)

sample1.4min (89%)

Algorithm

1×

intervals

Results

1.4min	3913×	body	8192	exit
2.6s	8000×	body	128	valid
237.0ms	11999×	pre	128	true
30.0ms	86×	body	128	invalid

Compiler

Compiled 733 to 617 computations (15.8% saved)

Details

analyze1.7s (1.8%)

sample2.9s (3%)

simplify211.0ms (0.2%)

prune23.0ms (0%)

localize61.0ms (0.1%)

rewrite67.0ms (0.1%)

series73.0ms (0.1%)

simplify72.0ms (0.1%)

prune1.1s (1.1%)

localize62.0ms (0.1%)

rewrite71.0ms (0.1%)

series88.0ms (0.1%)

simplify96.0ms (0.1%)

prune1.3s (1.4%)

localize55.0ms (0.1%)

rewrite103.0ms (0.1%)

series278.0ms (0.3%)

simplify60.0ms (0.1%)

prune656.0ms (0.7%)

localize57.0ms (0.1%)

rewrite220.0ms (0.2%)

series318.0ms (0.3%)

simplify122.0ms (0.1%)

prune899.0ms (0.9%)

regimes59.0ms (0.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4min (89%)

Profiling