Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

349×

body

valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	4
1	25	4
2	45	4
3	84	4
4	125	4
5	149	4
6	170	4
7	284	4
8	491	4
9	824	4
10	1344	4
11	2576	4
12	3873	4
13	5001	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 5.8b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ (* y (- z x)) t))
0.0b	(* y (- z x))
5.9b	(/ (* y (- z x)) t)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `associate-r` `add-log-exp`
4×	`associate-*r/`
3×	`times-frac` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

4.0ms	(+ x (/ (* y (- z x)) t))
6.0ms	(* y (- z x))
7.0ms	(/ (* y (- z x)) t)

series124.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ x (/ (* y (- z x)) t))
40.0ms	(* y (- z x))
48.0ms	(/ (* y (- z x)) t)

simplify38.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	290	325
1	1223	280
2	5001	280

prune120.0ms

Filtered

70 candidates to 45 candidates (64.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	9	71

Merged error: 0.0b

Counts

71 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
7.1b	(* (/ y (* (cbrt t) (cbrt t))) (/ (- z x) (cbrt t)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`times-frac`
38×	`*-un-lft-identity`
34×	`associate-r`
26×	`cbrt-prod` `add-cube-cbrt`
25×	`add-exp-log`
18×	`add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
4×	`add-log-exp`
3×	`pow1/3`
2×	`div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 104

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
24.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ (- z x) (cbrt t)))

series829.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt t)
380.0ms	(cbrt t)
177.0ms	(cbrt t)
95.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ (- z x) (cbrt t)))

simplify64.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	480	918
1	2615	741
2	5001	706

prune276.0ms

Filtered

116 candidates to 88 candidates (75.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	115	10	125

Merged error: 0.0b

Counts

125 → 10

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ t (- z x))
0.0b	(+ x (/ y (/ t (- z x))))
5.4b	(/ y (/ t (- z x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`*-un-lft-identity`
103×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 151

Calls

3 calls:

5.0ms	(/ t (- z x))
19.0ms	(+ x (/ y (/ t (- z x))))
13.0ms	(/ y (/ t (- z x)))

series119.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ t (- z x))
34.0ms	(+ x (/ y (/ t (- z x))))
57.0ms	(/ y (/ t (- z x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	539	1150
1	2368	1110
2	5001	1107

prune311.0ms

Filtered

160 candidates to 119 candidates (74.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	5	2	7
Picked	0	1	1
Done	1	1	2
Total	164	6	170

Merged error: 0b

Counts

170 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- z x))
0.5b	(cbrt (- z x))
1.6b	(/ y (/ t (cbrt (- z x))))
5.3b	(* (* (cbrt (- z x)) (cbrt (- z x))) (/ y (/ t (cbrt (- z x)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

353×	`times-frac`
228×	`add-sqr-sqrt`
219×	`*-un-lft-identity`
173×	`add-cube-cbrt`
116×	`cbrt-prod`
95×	`associate-r`
42×	`cbrt-div`
30×	`add-exp-log` `associate-/r*`
23×	`distribute-lft-out--` `difference-of-squares`
21×	`flip3--` `add-cbrt-cube` `flip--`
16×	`frac-times` `associate-/r/`
12×	`associate-*l/`
9×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
5×	`associate-*r/`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/l*`
2×	`pow1/3`
1×	`frac-2neg` `associate-l` `clear-num` `*-commutative`

Counts

4 → 307

Calls

4 calls:

3.0ms	(cbrt (- z x))
3.0ms	(cbrt (- z x))
11.0ms	(/ y (/ t (cbrt (- z x))))
36.0ms	(* (* (cbrt (- z x)) (cbrt (- z x))) (/ y (/ t (cbrt (- z x)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- z x))
149.0ms	(cbrt (- z x))
101.0ms	(/ y (/ t (cbrt (- z x))))
42.0ms	(* (* (cbrt (- z x)) (cbrt (- z x))) (/ y (/ t (cbrt (- z x)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1352	3576
1	5001	3427

prune846.0ms

Filtered

319 candidates to 264 candidates (82.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	319	6	325

Merged error: 0b

Counts

325 → 6

regimes165.0ms

Accuracy

25% (1.9b remaining)

Error of 1.9b against oracle of 0.0b and baseline of 2.6b

bsearch108.0ms

Steps

Iters	Range	Point
10	1.2853197318124835e-136	2.2305283447883118e-122	2.2207595967095594e-126
7	1.988366447315782e-219	2.0444912956939957e-217	6.914397869719574e-218
6	-2.2477448323498703e+18	-4.445579369187069e+17	-8.0051068491287e+17

Iters

Range

Point

1.2853197318124835e-136

2.2305283447883118e-122

2.2207595967095594e-126

1.988366447315782e-219

2.0444912956939957e-217

6.914397869719574e-218

-2.2477448323498703e+18

-4.445579369187069e+17

-8.0051068491287e+17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample586.0ms

Algorithm

intervals

Results

322.0ms

10639×

body

valid