Details

analyze16.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample118.0ms (0.1%)

Algorithm

1×

intervals

Results

56.0ms	62×	body	1024	valid
22.0ms	132×	body	128	valid
16.0ms	39×	body	512	valid
3.0ms	7×	body	2048	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify495.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune4.0ms (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: 29.9b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize13.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
1.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite142.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_2124`
88×	`times-frac_binary64_2130`
85×	`add-sqr-sqrt_binary64_2146`
37×	`add-cube-cbrt_binary64_2159`
34×	`cancel-sign-sub-inv_binary64_2090`
27×	`distribute-lft-out_binary64_2075`
22×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
11×	`associate-/r*_binary64_2068`
9×	`difference-of-sqr-1_binary64_2094`
7×	`associate-/l*_binary64_2069` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-/r/_binary64_2070`
5×	`add-log-exp_binary64_2163`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `pow1_binary64_2185` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-sub_binary64_2133`

Counts

3 → 147

Calls

3 calls:

87.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
16.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
10.0ms	(/.f64 x (+.f64 x 1))

series109.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
22.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
21.0ms	(/.f64 x (+.f64 x 1))

simplify153.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5658	2774

prune2.4s (2.3%)

Pruning

55 alts after pruning (54 fresh and 1 done)

	Pruned	Kept	Total
New	102	54	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	55	157

Merged error: 0.0b

Counts

157 → 55

Compiler

Compiled 4308 to 3114 computations (27.7% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
1.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
1.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite465.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`*-un-lft-identity_binary64_2124`
156×	`times-frac_binary64_2130`
136×	`add-sqr-sqrt_binary64_2146`
102×	`cancel-sign-sub-inv_binary64_2090`
70×	`exp-sum_binary64_2170`
52×	`add-cube-cbrt_binary64_2159`
51×	`distribute-lft-out--_binary64_2076`
49×	`distribute-lft-out_binary64_2075`
38×	`log-prod_binary64_2210`
36×	`difference-of-squares_binary64_2093`
32×	`exp-prod_binary64_2176`
17×	`log-pow_binary64_2213`
12×	`difference-of-sqr-1_binary64_2094`
9×	`add-log-exp_binary64_2163`
8×	`associate-/r/_binary64_2070`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r*_binary64_2068` `div-inv_binary64_2121`
3×	`associate-/l*_binary64_2069` `sub-neg_binary64_2117`
2×	`exp-diff_binary64_2172` `diff-log_binary64_2216` `rem-exp-log_binary64_2164`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `rem-log-exp_binary64_2165` `frac-sub_binary64_2133` `flip3-+_binary64_2127` `log-div_binary64_2211` `flip-+_binary64_2098` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 217

Calls

4 calls:

114.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
112.0ms	(exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
81.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
18.0ms	(/.f64 x (+.f64 x 1))

series292.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
100.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
60.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
26.0ms	(/.f64 x (+.f64 x 1))

simplify220.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5068	4560

prune3.7s (3.5%)

Pruning

94 alts after pruning (92 fresh and 2 done)

	Pruned	Kept	Total
New	183	46	229
Fresh	7	46	53
Picked	0	1	1
Done	0	1	1
Total	190	94	284

Merged error: 0.0b

Counts

284 → 94

Compiler

Compiled 6919 to 5119 computations (26% saved)

localize44.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.1b	(/.f64 1 (/.f64 (+.f64 x 1) x))
1.9b	(log.f64 (exp.f64 (-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
1.9b	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite1.0s (1%)

Algorithm

1×	rewrite-expression-head

Rules

275×	`*-un-lft-identity_binary64_2124`
255×	`times-frac_binary64_2130`
239×	`add-sqr-sqrt_binary64_2146`
102×	`cancel-sign-sub-inv_binary64_2090`
92×	`add-cube-cbrt_binary64_2159`
70×	`exp-sum_binary64_2170`
54×	`difference-of-squares_binary64_2093`
39×	`distribute-lft-out_binary64_2075`
38×	`log-prod_binary64_2210` `exp-prod_binary64_2176`
36×	`distribute-lft-out--_binary64_2076`
20×	`log-pow_binary64_2213`
16×	`associate-/r*_binary64_2068`
15×	`add-exp-log_binary64_2162`
12×	`difference-of-sqr-1_binary64_2094`
11×	`div-inv_binary64_2121`
9×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
7×	`associate-/r/_binary64_2070` `div-exp_binary64_2175`
6×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128`
3×	`cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069` `sub-neg_binary64_2117`
2×	`exp-diff_binary64_2172` `diff-log_binary64_2216` `rem-exp-log_binary64_2164` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `rem-log-exp_binary64_2165` `pow-flip_binary64_2198` `frac-sub_binary64_2133` `log-div_binary64_2211` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 281

Calls

4 calls:

299.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
299.0ms	(exp.f64 (-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
282.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
32.0ms	(/.f64 1 (/.f64 (+.f64 x 1) x))

series235.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
63.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
61.0ms	(exp.f64 (-.f64 (/.f64 1 (/.f64 (+.f64 x 1) x)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
25.0ms	(/.f64 1 (/.f64 (+.f64 x 1) x))

simplify250.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5009	6234

prune7.3s (7%)

Pruning

121 alts after pruning (118 fresh and 3 done)

	Pruned	Kept	Total
New	243	50	293
Fresh	23	68	91
Picked	0	1	1
Done	0	2	2
Total	266	121	387

Merged error: 0.0b

Counts

387 → 121

Compiler

Compiled 9880 to 7432 computations (24.8% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.1b	(/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x))
1.9b	(log.f64 (exp.f64 (-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
1.9b	(-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite2.2s (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

363×	`times-frac_binary64_2130`
331×	`*-un-lft-identity_binary64_2124`
328×	`add-sqr-sqrt_binary64_2146`
133×	`add-cube-cbrt_binary64_2159`
102×	`cancel-sign-sub-inv_binary64_2090`
75×	`sqrt-prod_binary64_2140`
70×	`exp-sum_binary64_2170`
66×	`difference-of-squares_binary64_2093`
48×	`distribute-lft-out_binary64_2075`
44×	`exp-prod_binary64_2176`
38×	`log-prod_binary64_2210`
33×	`distribute-lft-out--_binary64_2076`
23×	`log-pow_binary64_2213`
16×	`associate-/r*_binary64_2068`
12×	`difference-of-sqr-1_binary64_2094`
11×	`div-inv_binary64_2121`
9×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`associate-/r/_binary64_2070`
6×	`associate-/l*_binary64_2069`
5×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128`
3×	`cbrt-undiv_binary64_2158` `sub-neg_binary64_2117` `div-exp_binary64_2175`
2×	`exp-diff_binary64_2172` `diff-log_binary64_2216` `rem-exp-log_binary64_2164`
1×	`clear-num_binary64_2123` `rem-log-exp_binary64_2165` `frac-sub_binary64_2133` `log-div_binary64_2211` `frac-2neg_binary64_2135`

Counts

4 → 335

Calls

4 calls:

683.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
665.0ms	(exp.f64 (-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
587.0ms	(-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
50.0ms	(/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x))

series372.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
124.0ms	(-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
62.0ms	(exp.f64 (-.f64 (/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
23.0ms	(/.f64 (sqrt.f64 1) (/.f64 (+.f64 1 x) x))

simplify241.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

347 → 347

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4953	7750
1	4953	7750

prune10.9s (10.4%)

Pruning

135 alts after pruning (131 fresh and 4 done)

	Pruned	Kept	Total
New	318	29	347
Fresh	15	102	117
Picked	0	1	1
Done	0	3	3
Total	333	135	468

Merged error: 0.0b

Counts

468 → 135

Compiler

Compiled 8361 to 6177 computations (26.1% saved)

regimes6.8s (6.5%)

Compiler: Compiled 19178 to 15199 computations (20.7% saved)

bsearch37.8s (36.1%)

Steps

Iters	Range		Point
8	1621.1110225728203	5037975.795896405	14603.16566047444
11	-5.573097466288292e+23	-15.959237407043844	-10019.828485270371

Compiler

Compiled 1 to 1 computations (0% saved)

simplify22.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	92	63
1	92	63

end0.0ms (0%)

sample29.5s (28.1%)

Algorithm

1×

intervals

Results

712.0ms	1979×	body	1024	valid
446.0ms	4327×	body	128	valid
239.0ms	1021×	body	512	valid
89.0ms	490×	body	256	valid
57.0ms	183×	body	2048	valid

Compiler

Compiled 9398 to 7450 computations (20.7% saved)

Pareto

0.07587236422640412

Details

analyze16.0ms (0%)

sample118.0ms (0.1%)

simplify495.0ms (0.5%)

prune4.0ms (0%)

localize13.0ms (0%)

rewrite142.0ms (0.1%)

series109.0ms (0.1%)

simplify153.0ms (0.1%)

prune2.4s (2.3%)

localize20.0ms (0%)

rewrite465.0ms (0.4%)

series292.0ms (0.3%)

simplify220.0ms (0.2%)

prune3.7s (3.5%)

localize44.0ms (0%)

rewrite1.0s (1%)

series235.0ms (0.2%)

simplify250.0ms (0.2%)

prune7.3s (7%)

localize62.0ms (0.1%)

rewrite2.2s (2.1%)

series372.0ms (0.4%)

simplify241.0ms (0.2%)

prune10.9s (10.4%)

regimes6.8s (6.5%)

bsearch37.8s (36.1%)

simplify22.0ms (0%)

end0.0ms (0%)

sample29.5s (28.1%)

Profiling