Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	236×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1907	5
6	4560	5
7	5001	5

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 10.8b

Counts

2 → 2

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.1b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series152.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- y x) (- a t))
97.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	269	450
1	734	425
2	2488	423
3	5002	423

prune218.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 6.4b

Counts

72 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
15.1b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a t))
15.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series189.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1 (- a t))
56.0ms	(* (- y x) (/ 1 (- a t)))
97.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	351	602
1	1495	525
2	5001	481

prune290.0ms

Filtered

114 candidates to 69 candidates (60.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	114	11	125

Merged error: 6.4b

Counts

125 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.6b	(+ (* (- z t) (/ (- y x) (- a t))) x)
5.7b	(* (- z t) (/ (- y x) (- a t)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

13.0ms	(/ (- y x) (- a t))
14.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
19.0ms	(* (- z t) (/ (- y x) (- a t)))

series348.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- y x) (- a t))
158.0ms	(+ (* (- z t) (/ (- y x) (- a t))) x)
136.0ms	(* (- z t) (/ (- y x) (- a t)))

simplify63.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	490	904
1	2049	854
2	5001	852

prune366.0ms

Filtered

135 candidates to 95 candidates (70.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	135	11	146

Merged error: 4.2b

Counts

146 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
1.9b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t))))
7.1b	(+ (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t)))) x)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
38.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t))))
24.0ms	(+ (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t)))) x)

series835.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- a t))
160.0ms	(cbrt (- a t))
335.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t))))
184.0ms	(+ (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- y x) (cbrt (- a t)))) x)

simplify109.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	759	1907
1	3316	1731
2	5002	1632

prune513.0ms

Filtered

155 candidates to 112 candidates (72.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	155	11	166

Merged error: 4.2b

Counts

166 → 11

regimes282.0ms

Accuracy

21.3% (7.1b remaining)

Error of 10.7b against oracle of 3.7b and baseline of 12.7b

bsearch127.0ms

Steps

Iters	Range		Point
8	2.869351599928579e-140	7.727911359258938e-136	3.4384368107441154e-136
10	-9.434620063873919e-96	-6.642524222673344e-106	-2.3213324956078207e-103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms

sample733.0ms

Algorithm

intervals

Results

275.0ms	7753×	body	80	valid
61.0ms	483×	body	640	valid
50.0ms	289×	body	1280	valid
39.0ms	410×	body	320	valid
16.0ms	249×	body	160	valid
8.0ms	23×	body	2560	valid