Details

analyze1.0s (10.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.2%	87.6%	0.2%	13
21.8%	77.8%	0.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	223×	body	128	valid
2.0ms	18×	body	512	valid
2.0ms	47×	body	128	invalid
1.0ms	5×	body	1024	valid
1.0ms	9×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify266.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4887	19
1	4887	19

prune2.0ms (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: 22.7b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) (-.f64 t x))
1.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.5b	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_19343` `add-sqr-sqrt_binary64_19365`
13×	`flip--_binary64_19318` `flip3--_binary64_19347`
10×	`add-exp-log_binary64_19381` `add-cbrt-cube_binary64_19379`
9×	`add-cube-cbrt_binary64_19378`
8×	`frac-times_binary64_19353` `associate-/l/_binary64_19290`
6×	`cancel-sign-sub-inv_binary64_19309`
5×	`times-frac_binary64_19349` `associate-l_binary64_19284` `associate-r_binary64_19283` `add-log-exp_binary64_19382` `associate-/r*_binary64_19287` `pow1_binary64_19404`
4×	`difference-of-squares_binary64_19312` `distribute-rgt-in_binary64_19293` `associate-l/_binary64_19286` `associate-r/_binary64_19285` `distribute-lft-in_binary64_19292` `distribute-lft-out--_binary64_19295`
2×	`sub-neg_binary64_19336` `cbrt-unprod_binary64_19376` `prod-exp_binary64_19392` `associate-/r/_binary64_19289` `cbrt-undiv_binary64_19377` `div-exp_binary64_19394`
1×	`-commutative_binary64_19274` `sum-log_binary64_19434` `pow-prod-down_binary64_19414` `distribute-lft-out_binary64_19294` `unswap-sqr_binary64_19311` `frac-2neg_binary64_19354` `associate-/l_binary64_19288` `div-inv_binary64_19340` `clear-num_binary64_19342` `flip3-+_binary64_19346` `flip-+_binary64_19317` `+-commutative_binary64_19273`

Counts

3 → 85

Calls

3 calls:

16.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
15.0ms	(*.f64 (-.f64 y z) (-.f64 t x))
9.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series944.0ms (9.8%)

Counts

3 → 9

Calls

3 calls:

506.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
353.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
85.0ms	(*.f64 (-.f64 y z) (-.f64 t x))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	7021	1683

prune471.0ms (4.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 2.7b

Counts

95 → 9

Compiler

Compiled 9877 to 5597 computations (43.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.6b	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
2.3b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
6.3b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite94.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_19365`
78×	`*-un-lft-identity_binary64_19343`
60×	`cbrt-prod_binary64_19374`
54×	`associate-r_binary64_19283`
52×	`times-frac_binary64_19349`
34×	`add-cube-cbrt_binary64_19378`
28×	`cbrt-div_binary64_19375`
27×	`add-exp-log_binary64_19381`
25×	`associate-l_binary64_19284`
21×	`distribute-lft-out--_binary64_19295`
19×	`difference-of-squares_binary64_19312`
18×	`add-cbrt-cube_binary64_19379`
14×	`flip--_binary64_19318` `flip3--_binary64_19347`
13×	`pow1_binary64_19404`
10×	`swap-sqr_binary64_19310` `unswap-sqr_binary64_19311` `associate-/r/_binary64_19289`
9×	`cbrt-unprod_binary64_19376` `frac-times_binary64_19353` `prod-exp_binary64_19392`
7×	`pow1/3_binary64_19425` `cbrt-undiv_binary64_19377` `div-exp_binary64_19394`
6×	`add-log-exp_binary64_19382`
5×	`associate-l/_binary64_19286` `associate-r/_binary64_19285`
3×	`pow-prod-down_binary64_19414`
2×	`pow-prod-up_binary64_19413` `pow-sqr_binary64_19316` `*-commutative_binary64_19274` `div-inv_binary64_19340`
1×	`pow2_binary64_19424` `sum-log_binary64_19434` `pow-plus_binary64_19406` `flip3-+_binary64_19346` `flip-+_binary64_19317` `+-commutative_binary64_19273`

Counts

4 → 175

Calls

4 calls:

43.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
14.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
4.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
3.0ms	(cbrt.f64 (-.f64 a z))

series1.7s (17.9%)

Counts

4 → 12

Calls

4 calls:

752.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
518.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
233.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
220.0ms	(cbrt.f64 (-.f64 a z))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5712	4478

prune313.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	186	10	196

Merged error: 2.7b

Counts

196 → 10

Compiler

Compiled 8376 to 2934 computations (65% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
1.8b	(+.f64 x (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 1))
2.3b	(*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64_19365`
75×	`*-un-lft-identity_binary64_19343`
51×	`times-frac_binary64_19349`
31×	`associate-r_binary64_19283`
27×	`add-cube-cbrt_binary64_19378`
23×	`difference-of-squares_binary64_19312` `distribute-lft-out--_binary64_19295`
10×	`add-exp-log_binary64_19381` `add-cbrt-cube_binary64_19379`
5×	`associate-l_binary64_19284` `add-log-exp_binary64_19382` `flip--_binary64_19318` `associate-/l_binary64_19288` `associate-/r_binary64_19287` `pow1_binary64_19404` `flip3--_binary64_19347`
4×	`associate-/r/_binary64_19289`
2×	`unswap-sqr_binary64_19311` `div-inv_binary64_19340` `associate-*l/_binary64_19286` `cbrt-unprod_binary64_19376` `frac-times_binary64_19353` `associate-/l/_binary64_19290` `prod-exp_binary64_19392` `cbrt-undiv_binary64_19377` `div-exp_binary64_19394`
1×	`div-sub_binary64_19348` `-commutative_binary64_19274` `sum-log_binary64_19434` `pow-prod-down_binary64_19414` `distribute-lft-out_binary64_19294` `frac-2neg_binary64_19354` `clear-num_binary64_19342` `flip3-+_binary64_19346` `flip-+_binary64_19317` `+-commutative_binary64_19273` `associate-r/_binary64_19285`

Counts

3 → 120

Calls

3 calls:

21.0ms	(*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))
9.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
5.0ms	(+.f64 x (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 1))

series1.0s (10.4%)

Counts

3 → 9

Calls

3 calls:

522.0ms	(+.f64 x (pow.f64 (*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z))) 1))
386.0ms	(*.f64 (-.f64 t x) (/.f64 (-.f64 y z) (-.f64 a z)))
93.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4974	2424
1	4974	2424

prune148.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	130	9	139

Merged error: 2.7b

Counts

139 → 9

Compiler

Compiled 3776 to 1280 computations (66.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 y z))
0.6b	(cbrt.f64 (-.f64 y z))
1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))
2.6b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))))

rewrite69.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-exp-log_binary64_19381`
35×	`add-cbrt-cube_binary64_19379`
32×	`cbrt-unprod_binary64_19376` `prod-exp_binary64_19392`
22×	`cbrt-undiv_binary64_19377` `div-exp_binary64_19394`
15×	`*-un-lft-identity_binary64_19343` `add-sqr-sqrt_binary64_19365` `cbrt-prod_binary64_19374`
14×	`associate-l_binary64_19284`
9×	`pow1_binary64_19404` `add-cube-cbrt_binary64_19378`
8×	`times-frac_binary64_19349`
6×	`cbrt-div_binary64_19375` `add-log-exp_binary64_19382`
5×	`frac-times_binary64_19353` `associate-*r/_binary64_19285`
3×	`difference-of-squares_binary64_19312` `pow-prod-down_binary64_19414` `flip--_binary64_19318` `associate-*l/_binary64_19286` `flip3--_binary64_19347` `distribute-lft-out--_binary64_19295`
2×	`pow1/3_binary64_19425` `associate-/r/_binary64_19289`
1×	`associate-r_binary64_19283` `*-commutative_binary64_19274` `sum-log_binary64_19434` `div-inv_binary64_19340` `flip3-+_binary64_19346` `flip-+_binary64_19317` `+-commutative_binary64_19273`

Counts

4 → 103

Calls

4 calls:

41.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))
5.0ms	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))))
3.0ms	(cbrt.f64 (-.f64 y z))
3.0ms	(cbrt.f64 (-.f64 y z))

series1.7s (17.5%)

Counts

4 → 12

Calls

4 calls:

734.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z)))))
510.0ms	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))))
219.0ms	(cbrt.f64 (-.f64 y z))
212.0ms	(cbrt.f64 (-.f64 y z))

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4944	3350
1	4944	3350

prune109.0ms (1.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	115	9	124

Merged error: 2.7b

Counts

124 → 9

Compiler

Compiled 3952 to 558 computations (85.9% saved)

regimes140.0ms (1.5%)

Compiler: Compiled 1065 to 680 computations (36.2% saved)

bsearch62.0ms (0.6%)

Steps

Iters	Range		Point
9	2.0815813875174093e-163	1.7821673880283755e-155	5.632573208304651e-157
9	-5.873724201705015e-97	-7.764343139022992e-102	-7.87713316621998e-102

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	49
1	68	49

end0.0ms (0%)

sample1.0s (10.8%)

Algorithm

1×

intervals

Results

305.0ms	6720×	body	128	valid
57.0ms	378×	body	1024	valid
56.0ms	499×	body	512	valid
49.0ms	1204×	body	128	invalid
30.0ms	341×	body	256	valid
12.0ms	62×	body	2048	valid

Compiler

Compiled 297 to 186 computations (37.4% saved)

Details

analyze1.0s (10.8%)

sample28.0ms (0.3%)

simplify266.0ms (2.8%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite47.0ms (0.5%)

series944.0ms (9.8%)

simplify67.0ms (0.7%)

prune471.0ms (4.9%)

localize16.0ms (0.2%)

rewrite94.0ms (1%)

series1.7s (17.9%)

simplify77.0ms (0.8%)

prune313.0ms (3.3%)

localize11.0ms (0.1%)

rewrite49.0ms (0.5%)

series1.0s (10.4%)

simplify73.0ms (0.8%)

prune148.0ms (1.5%)

localize21.0ms (0.2%)

rewrite69.0ms (0.7%)

series1.7s (17.5%)

simplify102.0ms (1.1%)

prune109.0ms (1.1%)

regimes140.0ms (1.5%)

bsearch62.0ms (0.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.0s (10.8%)

Profiling