Details

sample28.0ms

Algorithm

intervals

Results

11.0ms	237×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	4×	body	1280	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (16.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	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: 9.3b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.2b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

6.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series115.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ y (- a t))
84.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify52.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	170	278
1	468	257
2	1400	257
3	5002	257

prune192.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	10	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 6.2b

Counts

57 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
11.1b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--` `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 → 99

Calls

3 calls:

6.0ms	(/ 1 (- a t))
11.0ms	(* y (/ 1 (- a t)))
1.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series149.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (- a t))
33.0ms	(* y (/ 1 (- a t)))
79.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify87.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	288	510
1	1143	440
2	4305	394
3	5001	391

prune243.0ms

Filtered

108 candidates to 65 candidates (60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	107	12	119

Merged error: 6.2b

Counts

119 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
2.6b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
11.3b	(* (/ y (- a t)) (- t z))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
47×	`add-cube-cbrt`
36×	`prod-diff`
31×	`times-frac`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
21×	`associate-l`
10×	`add-exp-log` `frac-add` `add-cbrt-cube`
8×	`flip3--` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`pow1` `associate-r` `associate-/r*`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `associate-l/` `sum-log` `log1p-expm1-u` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `fma-def` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

3 → 157

Calls

3 calls:

6.0ms	(/ y (- a t))
16.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
14.0ms	(* (/ y (- a t)) (- t z))

series307.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ y (- a t))
114.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
163.0ms	(* (/ y (- a t)) (- t z))

simplify121.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	859	1392
1	4016	1146
2	5001	1146

prune456.0ms

Filtered

166 candidates to 120 candidates (72.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	164	14	178

Merged error: 6.1b

Counts

178 → 14

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.9b	(+ (* y (/ (- t z) (- a t))) (+ x y))
2.0b	(* y (/ (- t z) (- a t)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

9.0ms	(/ (- t z) (- a t))
17.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))
15.0ms	(* y (/ (- t z) (- a t)))

series260.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- t z) (- a t))
142.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))
72.0ms	(* y (/ (- t z) (- a t)))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	529	835
1	2239	790
2	5002	788

prune294.0ms

Filtered

133 candidates to 91 candidates (68.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	5	7	12
Picked	0	1	1
Done	0	1	1
Total	136	11	147

Merged error: 3.3b

Counts

147 → 11

regimes423.0ms

Accuracy

34.6% (5.6b remaining)

Error of 8.8b against oracle of 3.3b and baseline of 11.8b

bsearch218.0ms

Steps

Iters	Range		Point
9	3.592876240554588e+159	9.074115100837207e+167	1.5064418940796455e+164
6	9.025014576781036	54.48611989218426	22.968365102893742
9	-2.1509734917177236e-96	-8.99297336972457e-103	-1.6881957529685786e-99
9	-6.371148359936497e+116	-1.510573042778816e+107	-2.317511083973365e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample686.0ms

Algorithm

intervals

Results

252.0ms	7347×	body	80	valid
63.0ms	491×	body	640	valid
41.0ms	271×	body	1280	valid
39.0ms	381×	body	320	valid
15.0ms	246×	body	160	valid
1.0ms	8×	body	2560	valid