Details

analyze639.0ms (18.8%)

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
3.1%	96.7%	0.2%	8
17.2%	82.7%	0.2%	9
21.8%	78%	0.2%	10
30%	68.8%	1.2%	11
31.8%	65.3%	2.9%	12
40.1%	55.3%	4.6%	13
44.5%	50.1%	5.4%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
2.0ms	61×	body	128	invalid

Compiler

Compiled 19 to 21 computations (-10.5% saved)

simplify56.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	704	13
1	704	13

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 1.6b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
6.1b	(*.f64 (/.f64 x y) (-.f64 z t))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-l_binary64`
12×	`cancel-sign-sub-inv_binary64`
10×	`times-frac_binary64`
8×	`associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

2 → 65

Calls

2 calls:

11.0ms	(*.f64 (/.f64 x y) (-.f64 z t))
10.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

series199.0ms (5.9%)

Counts

2 → 6

Calls

2 calls:

115.0ms	(*.f64 (/.f64 x y) (-.f64 z t))
84.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5066	1022

prune157.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	8	72

Merged error: 0.0b

Counts

72 → 8

Compiler

Compiled 3132 to 1527 computations (51.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 t (*.f64 (/.f64 x y) t))
0.0b	(+.f64 (.f64 z (/.f64 x y)) (-.f64 t (.f64 (/.f64 x y) t)))
4.0b	(*.f64 z (/.f64 x y))
4.6b	(*.f64 (/.f64 x y) t)

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64` `times-frac_binary64`
16×	`associate-r_binary64` `associate-l_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
8×	`pow1_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`associate-*r/_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `cancel-sign-sub-inv_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `associate-+r+_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-rgt-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

4 → 94

Calls

4 calls:

10.0ms	(*.f64 z (/.f64 x y))
9.0ms	(+.f64 (.f64 z (/.f64 x y)) (-.f64 t (.f64 (/.f64 x y) t)))
7.0ms	(*.f64 (/.f64 x y) t)
4.0ms	(-.f64 t (*.f64 (/.f64 x y) t))

series209.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(+.f64 (.f64 z (/.f64 x y)) (-.f64 t (.f64 (/.f64 x y) t)))
55.0ms	(-.f64 t (*.f64 (/.f64 x y) t))
39.0ms	(*.f64 z (/.f64 x y))
39.0ms	(*.f64 (/.f64 x y) t)

simplify59.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4976	1378
1	4976	1378

prune99.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

Compiler

Compiled 2301 to 608 computations (73.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 z (/.f64 x y)) (.f64 t (-.f64 1 (/.f64 x y))))
1.5b	(*.f64 t (-.f64 1 (/.f64 x y)))
4.0b	(*.f64 z (/.f64 x y))

rewrite49.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
52×	`cancel-sign-sub-inv_binary64`
48×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
28×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
21×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64` `associate-*r/_binary64`
6×	`associate-l_binary64`
5×	`add-log-exp_binary64` `div-inv_binary64`
4×	`sub-neg_binary64` `difference-of-squares_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `frac-add_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 126

Calls

3 calls:

14.0ms	(*.f64 t (-.f64 1 (/.f64 x y)))
13.0ms	(+.f64 (.f64 z (/.f64 x y)) (.f64 t (-.f64 1 (/.f64 x y))))
8.0ms	(*.f64 z (/.f64 x y))

series174.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

77.0ms	(+.f64 (.f64 z (/.f64 x y)) (.f64 t (-.f64 1 (/.f64 x y))))
61.0ms	(*.f64 t (-.f64 1 (/.f64 x y)))
36.0ms	(*.f64 z (/.f64 x y))

simplify46.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5028	1743

prune114.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	135	8	143

Merged error: 0.0b

Counts

143 → 8

Compiler

Compiled 2736 to 843 computations (69.2% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 z (/.f64 x y)) t) (.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) t))
0.2b	(*.f64 (neg.f64 x) (/.f64 1 y))
4.0b	(*.f64 z (/.f64 x y))
4.6b	(.f64 (.f64 (neg.f64 x) (/.f64 1 y)) t)

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
29×	`associate-r_binary64`
28×	`add-exp-log_binary64`
24×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
21×	`times-frac_binary64`
14×	`associate-l_binary64`
13×	`pow1_binary64`
12×	`prod-exp_binary64`
9×	`add-log-exp_binary64` `cbrt-unprod_binary64`
6×	`associate-*l/_binary64`
5×	`pow-prod-down_binary64` `associate-*r/_binary64` `distribute-lft-neg-out_binary64` `unswap-sqr_binary64`
4×	`frac-add_binary64` `un-div-inv_binary64`
3×	`flip3-+_binary64` `cbrt-undiv_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`
2×	`rec-exp_binary64` `div-inv_binary64`
1×	`associate-+l+_binary64` `neg-mul-1_binary64` `+-commutative_binary64` `unsub-neg_binary64`

Counts

4 → 117

Calls

4 calls:

11.0ms	(*.f64 (neg.f64 x) (/.f64 1 y))
11.0ms	(+.f64 (+.f64 (.f64 z (/.f64 x y)) t) (.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) t))
9.0ms	(.f64 (.f64 (neg.f64 x) (/.f64 1 y)) t)
8.0ms	(*.f64 z (/.f64 x y))

series194.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (+.f64 (.f64 z (/.f64 x y)) t) (.f64 (*.f64 (neg.f64 x) (/.f64 1 y)) t))
51.0ms	(.f64 (.f64 (neg.f64 x) (/.f64 1 y)) t)
33.0ms	(*.f64 z (/.f64 x y))
30.0ms	(*.f64 (neg.f64 x) (/.f64 1 y))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5688	1591

prune104.0ms (3.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	129	8	137

Merged error: 0.0b

Counts

137 → 8

Compiler

Compiled 2645 to 771 computations (70.9% saved)

regimes139.0ms (4.1%)

Compiler: Compiled 799 to 587 computations (26.5% saved)

bsearch43.0ms (1.3%)

Steps

Iters	Range		Point
8	1.554778019228192e-110	2.074857004379828e-106	7.139296702863165e-108
10	-3.797840194131708e+32	-9.672382885432595e+19	-1.5747647500589528e+20

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	60
1	101	60

end0.0ms (0%)

sample802.0ms (23.7%)

Algorithm

1×

intervals

Results

277.0ms	8000×	body	128	valid
78.0ms	2185×	body	128	invalid

Compiler

Compiled 202 to 134 computations (33.7% saved)

Details

analyze639.0ms (18.8%)

sample21.0ms (0.6%)

simplify56.0ms (1.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite26.0ms (0.8%)

series199.0ms (5.9%)

simplify65.0ms (1.9%)

prune157.0ms (4.6%)

localize8.0ms (0.2%)

rewrite37.0ms (1.1%)

series209.0ms (6.2%)

simplify59.0ms (1.7%)

prune99.0ms (2.9%)

localize10.0ms (0.3%)

rewrite49.0ms (1.4%)

series174.0ms (5.1%)

simplify46.0ms (1.3%)

prune114.0ms (3.4%)

localize12.0ms (0.4%)

rewrite50.0ms (1.5%)

series194.0ms (5.7%)

simplify67.0ms (2%)

prune104.0ms (3.1%)

regimes139.0ms (4.1%)

bsearch43.0ms (1.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample802.0ms (23.7%)

Profiling