Details

analyze342.0ms (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
12.5%	87.4%	0.1%	4
18.7%	81.1%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	78%	0.1%	7
27.3%	61.6%	11.1%	8
28.5%	60.5%	11.1%	9
32.6%	53.4%	14%	10
40.2%	38.1%	21.7%	11
41.8%	35.8%	22.4%	12
44.5%	29.2%	26.3%	13
47.1%	21.3%	31.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
7.0ms	200×	body	128	invalid

Compiler

Compiled 17 to 18 computations (-5.9% saved)

simplify262.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5335	12

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: 8.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(cosh.f64 x)
0.0b	(*.f64 (cosh.f64 x) (/.f64 y x))
7.5b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_15263`
17×	`add-exp-log_binary64_15277` `add-cbrt-cube_binary64_15275`
13×	`times-frac_binary64_15248` `associate-r_binary64_15184` `*-un-lft-identity_binary64_15242` `add-cube-cbrt_binary64_15274`
5×	`cbrt-undiv_binary64_15273` `pow1_binary64_15300` `cosh-def_binary64_15425` `div-exp_binary64_15290`
4×	`cbrt-unprod_binary64_15272` `prod-exp_binary64_15288`
3×	`associate-/l/_binary64_15191` `associate-l_binary64_15185` `add-log-exp_binary64_15278` `associate-/r*_binary64_15188`
2×	`div-inv_binary64_15239` `associate-r/_binary64_15186` `associate-l/_binary64_15187` `unswap-sqr_binary64_15210` `frac-times_binary64_15252`
1×	`-commutative_binary64_15175` `associate-/l_binary64_15189` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `pow-prod-down_binary64_15310`

Counts

3 → 68

Calls

3 calls:

8.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
8.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
1.0ms	(cosh.f64 x)

series483.0ms (10.6%)

Counts

3 → 9

Calls

3 calls:

269.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
159.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
55.0ms	(cosh.f64 x)

simplify81.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4943	985
1	4943	985

prune69.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	9	78

Merged error: 0.0b

Counts

78 → 9

Compiler

Compiled 1110 to 352 computations (68.3% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) y)
0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
6.1b	(/.f64 (.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) y) (.f64 z (*.f64 x 2)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64_15277` `add-cbrt-cube_binary64_15275`
10×	`cbrt-unprod_binary64_15272` `prod-exp_binary64_15288`
9×	`*-un-lft-identity_binary64_15242`
7×	`add-sqr-sqrt_binary64_15263`
6×	`cbrt-undiv_binary64_15273` `div-exp_binary64_15290`
5×	`associate-l_binary64_15185` `pow1_binary64_15300` `add-log-exp_binary64_15278` `add-cube-cbrt_binary64_15274`
4×	`associate-*l/_binary64_15187`
3×	`flip3-+_binary64_15245` `flip-+_binary64_15216` `associate-r_binary64_15184`
2×	`associate-/l/_binary64_15191` `distribute-lft-out_binary64_15195` `cosh-undef_binary64_15433`
1×	`-commutative_binary64_15175` `div-inv_binary64_15239` `times-frac_binary64_15248` `associate-/l_binary64_15189` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `pow-prod-down_binary64_15310` `sum-log_binary64_15330` `associate-/r*_binary64_15188` `unswap-sqr_binary64_15210` `+-commutative_binary64_15174`

Counts

3 → 62

Calls

3 calls:

16.0ms	(/.f64 (.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) y) (.f64 z (*.f64 x 2)))
9.0ms	(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) y)
6.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series337.0ms (7.4%)

Counts

3 → 9

Calls

3 calls:

218.0ms	(/.f64 (.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) y) (.f64 z (*.f64 x 2)))
93.0ms	(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) y)
26.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4981	1059
1	4981	1059

prune66.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 0.0b

Counts

80 → 9

Compiler

Compiled 1295 to 477 computations (63.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0b	(sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0b	(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
6.1b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) y) (.f64 z (.f64 x 2)))

rewrite79.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-exp-log_binary64_15277` `add-cbrt-cube_binary64_15275`
40×	`sqrt-prod_binary64_15257`
32×	`*-un-lft-identity_binary64_15242`
28×	`add-sqr-sqrt_binary64_15263` `sqrt-div_binary64_15258`
21×	`pow1_binary64_15300`
19×	`cbrt-unprod_binary64_15272` `prod-exp_binary64_15288`
14×	`flip3-+_binary64_15245` `flip-+_binary64_15216` `add-cube-cbrt_binary64_15274`
12×	`swap-sqr_binary64_15209` `associate-*l/_binary64_15187`
10×	`pow1/2_binary64_15319` `sqrt-pow1_binary64_15259`
9×	`cbrt-undiv_binary64_15273` `div-exp_binary64_15290`
8×	`associate-/l/_binary64_15191` `associate-l_binary64_15185` `distribute-lft-out_binary64_15195` `associate-r_binary64_15184` `frac-times_binary64_15252`
6×	`cosh-undef_binary64_15433`
5×	`pow-prod-up_binary64_15309`
4×	`associate-*r/_binary64_15186` `add-log-exp_binary64_15278` `unswap-sqr_binary64_15210`
3×	`pow-sqr_binary64_15215` `pow-prod-down_binary64_15310`
2×	`rem-sqrt-square_binary64_15255`
1×	`pow2_binary64_15320` `-commutative_binary64_15175` `sqrt-unprod_binary64_15261` `div-inv_binary64_15239` `times-frac_binary64_15248` `associate-/l_binary64_15189` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `rem-square-sqrt_binary64_15254` `associate-/r*_binary64_15188` `pow-plus_binary64_15302`

Counts

4 → 138

Calls

4 calls:

27.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) y) (.f64 z (.f64 x 2)))
19.0ms	(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
7.0ms	(sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
6.0ms	(sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series352.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) y) (.f64 z (.f64 x 2)))
57.0ms	(sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
56.0ms	(sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
29.0ms	(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5628	2548

prune192.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	149	10	159

Merged error: 0b

Counts

159 → 10

Compiler

Compiled 3642 to 1201 computations (67% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0b	(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z)
0.2b	(*.f64 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z) y)
7.0b	(/.f64 (.f64 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z) y) (.f64 x 2))

rewrite53.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_15242`
32×	`add-exp-log_binary64_15277` `times-frac_binary64_15248` `add-cbrt-cube_binary64_15275`
29×	`add-sqr-sqrt_binary64_15263`
24×	`add-cube-cbrt_binary64_15274`
19×	`associate-l_binary64_15185`
10×	`cbrt-undiv_binary64_15273` `div-exp_binary64_15290`
9×	`cbrt-unprod_binary64_15272` `prod-exp_binary64_15288`
8×	`distribute-lft-out_binary64_15195` `cosh-undef_binary64_15433`
6×	`pow1_binary64_15300` `associate-/l*_binary64_15189` `add-log-exp_binary64_15278`
4×	`associate-/r*_binary64_15188`
3×	`associate-/l/_binary64_15191` `div-inv_binary64_15239` `associate-r_binary64_15184`
2×	`flip3-+_binary64_15245` `flip-+_binary64_15216` `frac-2neg_binary64_15253` `clear-num_binary64_15241` `associate-*l/_binary64_15187` `unswap-sqr_binary64_15210`
1×	`*-commutative_binary64_15175` `pow-prod-down_binary64_15310` `sum-log_binary64_15330` `+-commutative_binary64_15174`

Counts

4 → 114

Calls

4 calls:

15.0ms	(/.f64 (.f64 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z) y) (.f64 x 2))
13.0ms	(*.f64 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z) y)
8.0ms	(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z)
5.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series534.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(/.f64 (.f64 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z) y) (.f64 x 2))
188.0ms	(*.f64 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z) y)
82.0ms	(/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) z)
24.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4983	2163
1	4983	2163

prune102.0ms (2.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	128	8	136

Merged error: 0b

Counts

136 → 8

Compiler

Compiled 2349 to 713 computations (69.6% saved)

regimes111.0ms (2.4%)

Compiler: Compiled 336 to 273 computations (18.8% saved)

bsearch62.0ms (1.4%)

Steps

Iters	Range		Point
9	13170360751.934975	4.5872945630696314e+17	741420780451993.0
4	-1.5121247063714074e+36	-9.109009467099694e+35	-9.905533536424995e+35

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	84
1	44	84

end0.0ms (0%)

sample1.1s (23.7%)

Algorithm

1×

intervals

Results

285.0ms	8000×	body	128	valid
250.0ms	7258×	body	128	invalid

Compiler

Compiled 204 to 142 computations (30.4% saved)

Details

analyze342.0ms (7.5%)

sample28.0ms (0.6%)

simplify262.0ms (5.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite22.0ms (0.5%)

series483.0ms (10.6%)

simplify81.0ms (1.8%)

prune69.0ms (1.5%)

localize12.0ms (0.3%)

rewrite37.0ms (0.8%)

series337.0ms (7.4%)

simplify59.0ms (1.3%)

prune66.0ms (1.4%)

localize17.0ms (0.4%)

rewrite79.0ms (1.7%)

series352.0ms (7.7%)

simplify63.0ms (1.4%)

prune192.0ms (4.2%)

localize15.0ms (0.3%)

rewrite53.0ms (1.2%)

series534.0ms (11.7%)

simplify84.0ms (1.9%)

prune102.0ms (2.2%)

regimes111.0ms (2.4%)

bsearch62.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (23.7%)

Profiling