Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample22.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	256×	pre	128	true
5.0ms	256×	body	128	valid

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify188.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	472	10
1	472	10

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: 8.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.5b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_2146`
28×	`*-un-lft-identity_binary64_2124`
19×	`times-frac_binary64_2130`
14×	`add-cube-cbrt_binary64_2159`
10×	`difference-of-squares_binary64_2093`
6×	`associate-/r*_binary64_2068`
5×	`distribute-lft-out--_binary64_2076`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`cancel-sign-sub-inv_binary64_2090` `associate-/l*_binary64_2069`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1_binary64_2185`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 58

Calls

2 calls:

18.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series111.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

61.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
50.0ms	(/.f64 x0 (-.f64 1 x1))

simplify53.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4939	940
1	4939	940

prune48.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	2	65

Merged error: 6.7b

Counts

65 → 2

Compiler

Compiled 896 to 538 computations (40% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.0b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite62.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_2124`
52×	`add-sqr-sqrt_binary64_2146`
22×	`add-cube-cbrt_binary64_2159`
19×	`times-frac_binary64_2130`
18×	`difference-of-squares_binary64_2093`
11×	`distribute-lft-out--_binary64_2076` `pow1_binary64_2185`
9×	`cancel-sign-sub-inv_binary64_2090`
8×	`flip--_binary64_2099` `flip3--_binary64_2128` `swap-sqr_binary64_2091` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-/r_binary64_2068` `associate-l_binary64_2065` `associate-r*_binary64_2064`
4×	`distribute-rgt-in_binary64_2074` `frac-times_binary64_2134` `distribute-lft-in_binary64_2073`
3×	`associate-/l*_binary64_2069` `sub-neg_binary64_2117`
2×	`associate-/r/_binary64_2070` `associate-l/_binary64_2067` `associate-r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `pow-prod-up_binary64_2194` `sum-log_binary64_2215` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `diff-log_binary64_2216` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `+-commutative_binary64_2054` `pow2_binary64_2205` `flip3-+_binary64_2127` `pow-sqr_binary64_2097` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 122

Calls

4 calls:

19.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
12.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series246.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
53.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
49.0ms	(/.f64 x0 (-.f64 1 x1))
16.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5082	1914

prune148.0ms (4.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 5.3b

Counts

136 → 2

Compiler

Compiled 3610 to 2238 computations (38% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (+.f64 x1 -2))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.0b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite46.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_2146`
36×	`*-un-lft-identity_binary64_2124`
19×	`times-frac_binary64_2130`
18×	`add-cube-cbrt_binary64_2159`
10×	`difference-of-squares_binary64_2093`
8×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`pow1_binary64_2185` `associate-/r*_binary64_2068`
5×	`distribute-lft-out--_binary64_2076`
4×	`associate-r_binary64_2064`
3×	`cancel-sign-sub-inv_binary64_2090` `associate-/l_binary64_2069` `associate-l*_binary64_2065`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `distribute-lft-out_binary64_2075` `associate-*r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `sum-log_binary64_2215` `*-commutative_binary64_2055` `diff-log_binary64_2216` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `distribute-rgt-in_binary64_2074` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 93

Calls

4 calls:

13.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
7.0ms	(*.f64 x1 (+.f64 x1 -2))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series290.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
61.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
45.0ms	(/.f64 x0 (-.f64 1 x1))
44.0ms	(*.f64 x1 (+.f64 x1 -2))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5413	1541

prune119.0ms (3.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 4.3b

Counts

107 → 2

Compiler

Compiled 2924 to 1828 computations (37.5% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
4.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
6.0b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite51.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_2146`
37×	`*-un-lft-identity_binary64_2124`
20×	`times-frac_binary64_2130`
19×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
8×	`add-log-exp_binary64_2163`
7×	`log-pow_binary64_2213` `log-prod_binary64_2210`
6×	`cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076` `associate-/r*_binary64_2068` `exp-prod_binary64_2176` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`exp-sum_binary64_2170`
3×	`associate-/l*_binary64_2069`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sub-neg_binary64_2117`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `rem-log-exp_binary64_2165` `sum-log_binary64_2215` `exp-diff_binary64_2172` `distribute-lft-out_binary64_2075` `diff-log_binary64_2216` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `log-div_binary64_2211` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 93

Calls

4 calls:

13.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
11.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
11.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series533.0ms (15.7%)

Counts

4 → 12

Calls

4 calls:

301.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
132.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
54.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
46.0ms	(/.f64 x0 (-.f64 1 x1))

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5117	1819

prune127.0ms (3.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 3.3b

Counts

107 → 2

Compiler

Compiled 3093 to 1993 computations (35.6% saved)

regimes152.0ms (4.5%)

Compiler: Compiled 2104 to 1562 computations (25.8% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	111
1	58	111

end0.0ms (0%)

sample941.0ms (27.7%)

Algorithm

1×

intervals

Results

223.0ms	8000×	pre	128	true
169.0ms	8000×	body	128	valid

Compiler

Compiled 553 to 409 computations (26% saved)

Details

analyze3.0ms (0.1%)

sample22.0ms (0.7%)

simplify188.0ms (5.5%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite29.0ms (0.8%)

series111.0ms (3.3%)

simplify53.0ms (1.6%)

prune48.0ms (1.4%)

localize10.0ms (0.3%)

rewrite62.0ms (1.8%)

series246.0ms (7.2%)

simplify61.0ms (1.8%)

prune148.0ms (4.3%)

localize13.0ms (0.4%)

rewrite46.0ms (1.3%)

series290.0ms (8.6%)

simplify67.0ms (2%)

prune119.0ms (3.5%)

localize16.0ms (0.5%)

rewrite51.0ms (1.5%)

series533.0ms (15.7%)

simplify47.0ms (1.4%)

prune127.0ms (3.7%)

regimes152.0ms (4.5%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample941.0ms (27.7%)

Profiling