Details

sample72.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
15.0ms	247×	body	80	nan

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
2.7b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.4b	(/ (* z (sqrt (+ t a))) t)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

21.0ms	(* z (sqrt (+ t a)))
7.0ms	(/ 2.0 (* t 3.0))
64.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
14.0ms	(/ (* z (sqrt (+ t a))) t)

series299.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* z (sqrt (+ t a)))
15.0ms	(/ 2.0 (* t 3.0))
158.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
71.0ms	(/ (* z (sqrt (+ t a))) t)

simplify51.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune879.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ t a)) t)
0.3b	(/ 2.0 (* t 3.0))
0.3b	(/ 2.0 (* t 3.0))
3.3b	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
27×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
13×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`sqrt-div` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 103

Calls

4 calls:

15.0ms	(/ (sqrt (+ t a)) t)
10.0ms	(/ 2.0 (* t 3.0))
7.0ms	(/ 2.0 (* t 3.0))
0.0ms	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (sqrt (+ t a)) t)
15.0ms	(/ 2.0 (* t 3.0))
14.0ms	(/ 2.0 (* t 3.0))
186.0ms	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	378	688
1	1172	613
2	5001	603

prune588.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
0.3b	(/ 2.0 (* t 3.0))
1.6b	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0))))))))
3.8b	(log (exp (/ 2.0 (* t 3.0))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`log-pow`
7×	`exp-prod`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 77

Calls

4 calls:

8.0ms	(/ 2.0 (* t 3.0))
7.0ms	(/ 2.0 (* t 3.0))
0.0ms	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0))))))))
9.0ms	(log (exp (/ 2.0 (* t 3.0))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 2.0 (* t 3.0))
15.0ms	(/ 2.0 (* t 3.0))
188.0ms	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0))))))))
16.0ms	(log (exp (/ 2.0 (* t 3.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	233	465
1	661	393
2	2394	391
3	5002	387

prune532.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c 0.8333333333333334 (* a (- c b)))
0.0b	(- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))
0.0b	(exp (* 2.0 (+ (fma c 0.8333333333333334 (* a (- c b))) (* (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))) (+ (- (- b c)) (- b c))))))
0.3b	(/ 2.0 (* t 3.0))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
28×	`prod-diff`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
15×	`times-frac`
11×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`associate-/l*`
2×	`cbrt-undiv` `diff-log` `div-exp` `exp-sum` `frac-sub` `distribute-lft-out--`
1×	`distribute-rgt-in` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `frac-2neg` `distribute-lft-in` `flip3-+` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `sum-log` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `rem-exp-log` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

0.0ms	(fma c 0.8333333333333334 (* a (- c b)))
100.0ms	(- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))
5.0ms	(exp (* 2.0 (+ (fma c 0.8333333333333334 (* a (- c b))) (* (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))) (+ (- (- b c)) (- b c))))))
7.0ms	(/ 2.0 (* t 3.0))

series111.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma c 0.8333333333333334 (* a (- c b)))
18.0ms	(- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))
44.0ms	(exp (* 2.0 (+ (fma c 0.8333333333333334 (* a (- c b))) (* (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))) (+ (- (- b c)) (- b c))))))
15.0ms	(/ 2.0 (* t 3.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	515	1263
1	1797	959
2	5001	927

prune387.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes304.0ms

Accuracy

0.5% (1.8b remaining)

Error of 2.3b against oracle of 0.5b and baseline of 2.3b

bsearch376.0ms

Steps

Iters	Range		Point
10	1.0363137024699586e-249	1.2765857967054786e-239	2.4237249595871114e-244
9	-2.574369336412057e-106	-2.2227179944151216e-115	-8.15629739142147e-111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	62
1	87	62
2	87	62

end0.0ms

sample1.9s

Algorithm

intervals

Results

537.0ms	8000×	body	80	valid
510.0ms	8126×	body	80	nan