Details

analyze13.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample22.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify238.0ms (10.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5184	22

prune2.0ms (0.1%)

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: 20.9b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
20.6b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite24.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1058`
7×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
5×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
4×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `frac-times_binary64_1121` `add-cube-cbrt_binary64_1146` `add-log-exp_binary64_1150`
3×	`times-frac_binary64_1117` `associate-/r*_binary64_1055` `flip3--_binary64_1115` `flip--_binary64_1086`
2×	`associate-l/_binary64_1054` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `pow1_binary64_1172` `associate-r/_binary64_1053` `associate-/r/_binary64_1057`
1×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `associate-/l*_binary64_1056` `+-commutative_binary64_1041` `sum-log_binary64_1202` `clear-num_binary64_1110`

Counts

2 → 42

Calls

2 calls:

15.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series130.0ms (5.6%)

Counts

2 → 6

Calls

2 calls:

90.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
40.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify33.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5033	969

prune70.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Merged error: 0.4b

Counts

49 → 5

Compiler

Compiled 1622 to 476 computations (70.7% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Merged error: 0.4b

Counts

5 → 5

Compiler

Compiled 67 to 33 computations (50.7% saved)

localize12.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.2b	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
19.7b	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))

rewrite42.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_1111`
28×	`add-sqr-sqrt_binary64_1133`
25×	`times-frac_binary64_1117`
21×	`add-cube-cbrt_binary64_1146`
18×	`associate-r_binary64_1051`
10×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
7×	`distribute-lft-out_binary64_1062`
5×	`associate-l_binary64_1052` `add-log-exp_binary64_1150` `pow1_binary64_1172`
4×	`flip-+_binary64_1085` `associate-/l*_binary64_1056` `flip3-+_binary64_1114` `associate-/r/_binary64_1057`
3×	`associate-/r*_binary64_1055`
2×	`prod-exp_binary64_1160` `associate-*l/_binary64_1054` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `frac-times_binary64_1121` `flip3--_binary64_1115` `associate-/l/_binary64_1058` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `unswap-sqr_binary64_1079` `flip--_binary64_1086`
1×	`-commutative_binary64_1042` `frac-2neg_binary64_1122` `+-commutative_binary64_1041` `pow-prod-down_binary64_1182` `difference-of-squares_binary64_1080` `sum-log_binary64_1202` `clear-num_binary64_1110` `distribute-lft-out--_binary64_1063` `associate-r/_binary64_1053`

Counts

3 → 89

Calls

3 calls:

19.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
9.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series178.0ms (7.7%)

Counts

3 → 9

Calls

3 calls:

80.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
57.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))
41.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify60.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5348	2173

prune81.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	98	5	103

Merged error: 0.4b

Counts

103 → 5

Compiler

Compiled 2527 to 454 computations (82% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
20.6b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite51.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_1117` `exp-prod_binary64_1163`
30×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
19×	`log-pow_binary64_1200`
10×	`difference-of-squares_binary64_1080`
7×	`add-log-exp_binary64_1150`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149` `associate-/r/_binary64_1057`
5×	`pow1_binary64_1172`
4×	`flip-+_binary64_1085` `associate-/l*_binary64_1056` `flip3-+_binary64_1114`
3×	`log-prod_binary64_1197` `div-inv_binary64_1108` `associate-/r*_binary64_1055` `div-sub_binary64_1116`
2×	`exp-diff_binary64_1159` `associate-/l/_binary64_1058`
1×	`frac-2neg_binary64_1122` `flip3--_binary64_1115` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `rem-exp-log_binary64_1151` `log-div_binary64_1198` `sum-log_binary64_1202` `rem-log-exp_binary64_1152` `clear-num_binary64_1110` `flip--_binary64_1086`

Counts

4 → 105

Calls

4 calls:

11.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
10.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
10.0ms	(exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
8.0ms	(+.f64 (.f64 x x) (.f64 y y))

series285.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))))
81.0ms	(exp.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))))
67.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
37.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify82.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4945	2859
1	4945	2859

prune89.0ms (3.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	117	5	122

Merged error: 0.4b

Counts

122 → 5

Compiler

Compiled 3055 to 402 computations (86.8% saved)

regimes50.0ms (2.1%)

Compiler: Compiled 144 to 84 computations (41.7% saved)

bsearch49.0ms (2.1%)

Steps

Iters	Range	Point
9	2.2994220296459768e-157	6.565353910433547e-152	2.3252284660370693e-157
10	-1.3245229100896109e-157	-1.449328662951762e-172	-1.5986692674923848e-162
6	-3.393854872623411e-39	-7.843104225007375e-40	-3.345932334055194e-39

Iters

Range

Point

2.2994220296459768e-157

6.565353910433547e-152

2.3252284660370693e-157

-1.3245229100896109e-157

-1.449328662951762e-172

-1.5986692674923848e-162

-3.393854872623411e-39

-7.843104225007375e-40

-3.345932334055194e-39

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	48
1	43	48

end0.0ms (0%)

sample769.0ms (33.2%)

Algorithm

1×

intervals

Results

304.0ms	8000×	body	128	valid
163.0ms	8000×	pre	128	true

Compiler

Compiled 161 to 98 computations (39.1% saved)

Details

analyze13.0ms (0.5%)

sample22.0ms (1%)

simplify238.0ms (10.3%)

prune2.0ms (0.1%)

localize9.0ms (0.4%)

rewrite24.0ms (1%)

series130.0ms (5.6%)

simplify33.0ms (1.4%)

prune70.0ms (3%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.3%)

prune4.0ms (0.2%)

localize12.0ms (0.5%)

rewrite42.0ms (1.8%)

series178.0ms (7.7%)

simplify60.0ms (2.6%)

prune81.0ms (3.5%)

localize11.0ms (0.5%)

rewrite51.0ms (2.2%)

series285.0ms (12.3%)

simplify82.0ms (3.5%)

prune89.0ms (3.9%)

regimes50.0ms (2.1%)

bsearch49.0ms (2.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample769.0ms (33.2%)

Profiling